2013

We introduce Puppet Flow (PF), a layered model describing the optical flow of a person in a video sequence. We consider video frames composed by two layers: a foreground layer corresponding to a person, and background.
We model the background as an affine flow field. The foreground layer, being a moving person, requires reasoning about the articulated nature of the human body. We thus represent the foreground layer with the Deformable Structures model (DS), a parametrized 2D part-based human body representation. We call the motion field defined through articulated motion and deformation of the DS model, a Puppet Flow. By exploiting the DS representation, Puppet Flow is a parametrized optical flow field, where parameters are the person's pose, gender and body shape.

In many naturally occurring optimization problems one needs to ensure that the definition of the optimization problem lends itself to solutions that are tractable to compute. In cases where exact solutions cannot be computed tractably, it is beneficial to have strong guarantees on the tractable approximate solutions. In order operate under these criterion most optimization problems are cast under the umbrella of convexity or submodularity. In this report we will study design and optimization over a common class of functions called submodular functions. Set functions, and specifically submodular set functions, characterize a wide variety of naturally occurring optimization problems, and the property of submodularity of set functions has deep theoretical consequences with wide ranging applications. Informally, the property of submodularity of set functions concerns the intuitive principle of diminishing returns. This property states that adding an element to a smaller set has more value than adding it to a larger set. Common examples of submodular monotone functions are entropies, concave functions of cardinality, and matroid rank functions; non-monotone examples include graph cuts, network flows, and mutual information. In this paper we will review the formal definition of submodularity; the optimization of submodular functions, both maximization and minimization; and finally discuss some applications in relation to learning and reasoning using submodular functions.

We present two alternative ways to apply PAC-Bayesian analysis to sequences of dependent random variables. The first is based on a new lemma that enables to bound expectations of convex functions of certain dependent random variables by expectations of the same functions of independent Bernoulli random variables. This lemma provides an alternative tool to Hoeffding-Azuma inequality to bound concentration of martingale values. Our second approach is based on integration of Hoeffding-Azuma inequality with PAC-Bayesian analysis. We also introduce a way to apply PAC-Bayesian analysis in situation of limited feedback. We combine the new tools to derive PAC-Bayesian generalization and regret bounds for the multiarmed bandit problem. Although our regret bound is not yet as tight as state-of-the-art regret bounds based on other well-established techniques, our results significantly expand the range of potential applications of PAC-Bayesian analysis and introduce a new analysis tool to reinforcement learning and many other fields, where martingales and limited feedback are encountered.

Taking a sharp photo at several megapixel resolution traditionally
relies on high grade lenses. In this paper, we present an approach to alleviate
image degradations caused by imperfect optics. We rely on a calibration step
to encode the optical aberrations in a space-variant point spread function and
obtain a corrected image by non-stationary deconvolution. By including the
Bayer array in our image formation model, we can perform demosaicing as part
of the deconvolution.

We present a probabilistic viewpoint to multiple kernel learning unifying well-known regularised risk approaches and recent advances in approximate Bayesian inference relaxations. The framework proposes a general objective function suitable for regression, robust regression and classification that is lower bound of the marginal likelihood and contains many regularised risk approaches as special cases. Furthermore, we derive an efficient and provably convergent optimisation algorithm.

We study statistical detection of grayscale objects in noisy images. The object of
interest is of unknown shape and has an unknown intensity, that can be varying over the object
and can be negative. No boundary shape constraints are imposed on the object, only a weak bulk
condition for the object's interior is required. We propose an algorithm that can be used to detect
grayscale objects of unknown shapes in the presence of nonparametric noise of unknown level. Our
algorithm is based on a nonparametric multiple testing procedure.
We establish the limit of applicability of our method via an explicit, closed-form, non-asymptotic
and nonparametric consistency bound. This bound is valid for a wide class of nonparametric noise
distributions. We achieve this by proving an uncertainty principle for percolation on nite lattices.

Within the unmanageably large class of nonconvex optimization, we consider the rich subclass of nonsmooth problems having composite objectives (this includes the extensively studied convex, composite objective problems as
a special case). For this subclass, we introduce a powerful, new framework that permits asymptotically non-vanishing perturbations. In particular, we develop perturbation-based batch and incremental (online like) nonconvex proximal splitting algorithms. To our knowledge, this is the rst time that such perturbation-based nonconvex splitting algorithms are being proposed and analyzed. While the main contribution of the paper is the theoretical framework, we complement our results by presenting some empirical results on matrix factorization.

Our goal is to understand the principles of Perception, Action and Learning in autonomous systems that successfully interact with complex environments and to use this understanding to design future systems